Mathematical Research Letters

Volume 13 (2006)

Number 6

Asymptotics of orthogonal polynomials via the Koosis theorem

Pages: 975 – 983

DOI: http://dx.doi.org/10.4310/MRL.2006.v13.n6.a12

Authors

F. Nazarov (Michigan State University)

A. Volberg (Michigan State University)

P. Yuditskii (Bar Ilan University)

Abstract

The main aim of this short paper is to advertise the Koosis theorem in the mathematical community, especially among those who study orthogonal polynomials. We (try to) do this by proving a new theorem about asymptotics of orthogonal polynomials for which the Koosis theorem seems to be the most natural tool. Namely, we consider the case when a Szegö measure on the unit circumference is perturbed by an arbitrary measure inside the unit disk and an arbitrary Blaschke sequence of point masses outside the unit disk.